Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function
The literature has an astonishingly large number of integral formulae involving a range of special functions. In this paper, by using three Beta function formulae, we aim to establish three integral formulas whose integrands are products of the generalized hypergeometric series p+1Fp and the integra...
| Main Authors: | , , , |
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| Format: | Article |
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MDPI
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/100648/ |
| _version_ | 1848863378730123264 |
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| author | Choi, Junesang Kurumujji, Shantha Kumari Kilicman, Adem Rathie, Arjun Kumar |
| author_facet | Choi, Junesang Kurumujji, Shantha Kumari Kilicman, Adem Rathie, Arjun Kumar |
| author_sort | Choi, Junesang |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The literature has an astonishingly large number of integral formulae involving a range of special functions. In this paper, by using three Beta function formulae, we aim to establish three integral formulas whose integrands are products of the generalized hypergeometric series p+1Fp and the integrands of the three Beta function formulae. Among the many particular instances for our formulae, several are stated clearly. Moreover, an intriguing inequality that emerges throughout the proving procedure is shown. It is worth noting that the three integral formulae shown here may be expanded further by using a variety of more generalized special functions than p+1Fp. Symmetry occurs naturally in the Beta and p+1Fp functions, which are two of the most important functions discussed in this study. |
| first_indexed | 2025-11-15T13:31:58Z |
| format | Article |
| id | upm-100648 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:31:58Z |
| publishDate | 2022 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1006482023-09-21T08:03:43Z http://psasir.upm.edu.my/id/eprint/100648/ Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function Choi, Junesang Kurumujji, Shantha Kumari Kilicman, Adem Rathie, Arjun Kumar The literature has an astonishingly large number of integral formulae involving a range of special functions. In this paper, by using three Beta function formulae, we aim to establish three integral formulas whose integrands are products of the generalized hypergeometric series p+1Fp and the integrands of the three Beta function formulae. Among the many particular instances for our formulae, several are stated clearly. Moreover, an intriguing inequality that emerges throughout the proving procedure is shown. It is worth noting that the three integral formulae shown here may be expanded further by using a variety of more generalized special functions than p+1Fp. Symmetry occurs naturally in the Beta and p+1Fp functions, which are two of the most important functions discussed in this study. MDPI 2022-02-15 Article PeerReviewed Choi, Junesang and Kurumujji, Shantha Kumari and Kilicman, Adem and Rathie, Arjun Kumar (2022) Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function. Symmetry, 14 (2). art. no. 389. pp. 1-13. ISSN 2073-8994 https://www.mdpi.com/2073-8994/14/2/389 10.3390/sym14020389 |
| spellingShingle | Choi, Junesang Kurumujji, Shantha Kumari Kilicman, Adem Rathie, Arjun Kumar Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function |
| title | Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function |
| title_full | Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function |
| title_fullStr | Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function |
| title_full_unstemmed | Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function |
| title_short | Certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function |
| title_sort | certain integral formulae associated with the product of generalized hypergeometric series and several elementary functions derived from formulas for the beta function |
| url | http://psasir.upm.edu.my/id/eprint/100648/ http://psasir.upm.edu.my/id/eprint/100648/ http://psasir.upm.edu.my/id/eprint/100648/ |